Tarski Grothendieck Set Theory

Andrzej Trybulec

Warsaw University Bialystok

Supported by RPBP.III-24.B1.

Summary.

This is the first part of the axiomatics of the Mizar system. It includes
the axioms of the Tarski Grothendieck set theory. They are:
the axiom stating that everything is a set,
the extensionality axiom,
the definitional axiom of the singleton,
the definitional axiom of the pair,
the definitional axiom of the union of a family of sets,
the definitional axiom of the boolean (the power set) of a set,
the regularity axiom,
the definitional axiom of the ordered pair,
the Tarski's axiom~A introduced in [1] (see also [2]),
and the Fr\ae nkel scheme.
Also, the definition of equinumerosity is introduced.